Bay Area Mathematical Artists, VI

As I mentioned last time, this meeting took place at Santa Clara University.  As we have several participants in the South Bay area, many appreciated the shorter drive…it turns out this was the most well-attended event to date.  Even better, thanks to Frank, the Mathematics and Computer Science Department at Santa Clara University provided wonderful pastries, coffee, and juice for all!

Our first speaker was Frank A. Farris, our host at Santa Clara University.  (Recall that last month, he presented a brief preview of his talk.)  His talk was about introducing a sound element into his wallpaper patterns.

In order to do this, he used frequencies based on the spectrum of hexagonal and square grids.  It’s not important to know what this means — the main idea is that you get frequencies that are not found in western music.

Frank’s idea was to take his wallpaper patterns, and add music to them using these non-traditional frequencies.  Here is a screenshot from one of his musical movies:


Frank was really excited to let us know that the San Jose Chamber Orchestra commissioned work by composer William Susman to accompany his moving wallpaper patterns.  The concert will take place in a few weeks; here is the announcement, so you are welcome to go listen for yourself!

Day135susman_farris invite_18

Frank has extensive information about his work on his website, and even software you can download to make your very own wallpaper patterns.  Feel free to email him with any questions you might have at

The second talk, Salvador Dali — Old and New, was given by Tom Banchoff, retired from Brown University.  He fascinated us with the story of his long acquaintance with Salvador Dali.  It all began with an interview in 1975 with the Washington Post about Tom’s work in visualizing the fourth dimension.

He was surprised to see that the day after the interview, the article Visual Images And Shadows From The Fourth Dimension in the next day’s Post, as well as a picture of Dali’s Corpus Hypercubus (1954).

Salvador Dali’s Crucifixion (Corpus Hypercubus)

But Tom was aware that Dali was very particular about giving permission to use his work in print, and knew that the Post didn’t have time to get this permission in such a short time frame.

The inevitable call came from New York — Dali wanted to meet Tom.  He wondered whether Dali was simply perturbed that a photo of his work was used without permission — but luckily, that was not the reason for setting up the meeting at all.  Dali was interested in creating stereoscopic oil paintings, and stereoscopic images were mentioned in the Post article.

Thus began Tom’s long affiliation with Dali.  He mentioned meeting Dali eight or nine times in New York (Dali came to New York every Spring to work), three times in Spain, and once in France.  Tom remarked that Dali was the most fascinating person he’d ever met — and that includes mathematicians!

Tom with Salvador Dali.

Then Tom proceeded to discuss the genesis of Corpus Hypercubus.  His own work included collaboration with Charles Strauss at Brown University, which included rendering graphics to help visualize the fourth dimension — but this was back in the 1960’s, when computer technology was at its infancy.  It was a lot more challenging then than it would be today to create the same videos.

Tom’s rendition of a hypercube net.

He also spent some time discussing a net for the hypercube, since a hypercube net is the geometrical basis for Dali’s Corpus Hypercubus.  What makes understanding the fourth dimension difficult is imagining how this net goes together.

It is not hard to imagine folding a flat net of six squares to make a cube — but in order to do that, we need to fold some of the squares up through the third dimension.  But to fold the hypercube net to make a hypercube without distorting the cubes requires folding the cubes up into a fourth spatial dimension.

This is difficult to imagine!  Needless to say, this was a very interesting discussion, and challenged participants to definitely think outside the box.

Tom remarked that Dali’s interest in the hypercube was inspired by the work of Juan de Herrera (1530-1597), who was in turn inspired by Ramon Lull (1236-1315).

Tom also mentioned an unusual project Dali was interested in near the end of his career.  He wanted to design a horse that when looked at straight on, looks like a front view of a horse.  But when looked from the side, it’s 300 meters long!  For more information, feel free to email Tom at

Dali’s sketch of the horse.

Suffice it to say that we all enjoyed Frank’s and Tom’s presentations.  The change of venue was welcome, and we hope to be at Santa Clara again in the future.

Following the talks, Frank generously invited us to his home for a potluck dinner!  He provided lasagna and eggplant parmigiana, while the rest of us provided appetizers, salads, side dishes, and desserts.

As usual, the conversation was quite lively!  We talked for well over two hours, but many of us had a bit of a drive, so we eventually needed to make our collective ways home.

Next time, on April 7, we’ll be back at the University of San Francisco.  At this meeting, we’ll go back to shorter talks in order to give several participants a chance to participate.  Stay tuned for a summary of next month’s talks!

Published by

Vince Matsko

Mathematician, educator, consultant, artist, puzzle designer, programmer, blogger, etc., etc. @cre8math

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